The European Physical Journal Special Topics

, Volume 223, Issue 14, pp 3287–3293

Ageing single file motion

  • R. Metzler
  • L. Sanders
  • M. A. Lomholt
  • L. Lizana
  • K. Fogelmark
  • Tobias Ambjörnsson
Regular Article
Part of the following topical collections:
  1. Brownian Motion in Confined Geometries. Guest Editors: S.M. Bezrukov, L. Schimansky-Geier and G. Schmid (Eds.)

Abstract

The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling 〈x2(t)〉 ≃ K1/2t1/2 as function of time. Here we study what happens to this law when each particle of the single file interacts with the environment such that it is transiently immobilised for times τ with a power-law distribution ψ(τ) ≃ (τ)α, and different ranges of the exponent α are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris’ law to an ultraslow, logarithmic time evolution 〈x2(t)〉 ≃ K0 log 1/2(t) when 0 < α < 1. In the intermediate case 1 < α < 2, we observe a power-law form for the mean squared displacement, with a modified scaling exponent as compared to Harris’ law. Once α is larger than two, the Brownian single file behaviour and thus Harris’ law are restored. We also point out that this process is weakly non-ergodic in the sense that the time and ensemble averaged mean squared displacements are disparate.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  • R. Metzler
    • 1
    • 2
  • L. Sanders
    • 3
  • M. A. Lomholt
    • 4
  • L. Lizana
    • 5
  • K. Fogelmark
    • 3
  • Tobias Ambjörnsson
    • 3
  1. 1.Institute of Physics & AstronomyUniversity of PotsdamPotsdam-GolmGermany
  2. 2.Department of PhysicsTampere University of TechnologyTampereFinland
  3. 3.Department of Astronomy and Theoretical PhysicsLund UniversityLundSweden
  4. 4.MEMPHYS - Center for Biomembrane Physics, Department of Physics, Chemistry, and PharmacyUniversity of Southern DenmarkOdenseDenmark
  5. 5.Integrated Science Lab, Department of PhysicsUmeå UniversityUmeåSweden

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